低频大气声重波的非线性Schr?dinger方程

本文采用多重时空尺度展开的方法,对于不可压缩等温大气,导出了二维情况下低频声重波的非线性Schr?dinger方程,讨论了声重波的非线性性质.在垂直方向上,声重波具有可传播性和幅度随高度增长的特性;在水平方向上,声重波能表现为孤子包络调制的波列.     

低频大气声重波的非线性Schrdinger方程

本文采用多重时空尺度展开的方法,对于不可压缩等温大气,导出了二维情况下低频声重波的非线性Schrdinger方程,讨论了声重波的非线性性质.在垂直方向上,声重波具有可传播性和幅度随高度增长的特性;在水平方向上,声重波能表现为孤子包络调制的波列.     

完整Coriolis力作用下的二维非线性Rossby波

本文在正压流体中,从包含完整Coriolis参数的准地转位涡方程出发,在弱非线性长波近似下,采用多时空尺度和摄动方法,推导出大气非线性Rossby波振幅演变满足带有地形强迫的非线性Zakharov-Kuznetsov(ZK)-Burgers方程.结果分析表明:地球旋转的水平分量、β效应、地形效应和耗散都是诱导二维Rossby波产生的重要因子.     

非线性P波在二维固体中的传播特点数值模拟

波动理论一直是地震学的核心内容,非线性波在介质中是真实存在的,能够充分认识非线性波,将对波动理论的发展和进一步应用提供很大的帮助.本文从固体介质中的位移、应力、应变的基本关系出发,推导了非线性P波在二维固体中的传播的非线性方程,对此非线性方程,采用四阶差分的方法,研究其在二维空间中的传播特点,对非线性波的传播有了更深的认识和理解.     

时空变化风场中声重波波包的演变

本文从可压缩情况下的流体力学方程出发,采用多重尺度方法和W.K.B.方法,研究时空变化风场中声重波波包的演变过程。文中导出了声重波波长、相速、传播方向以及振幅的演变方程。结果表明,沿群路径上波长、相速和传播方向的变化取决于风场的时空变化以及风场与波的相对方位。此外,波振幅的演变方程还表明:在时空慢变风场中,声重波的波作用量具有守恒性,声重波波包能量增加伴随波频率增高,声重波波包能量减小伴随频率降低。能量变化的实质是,风场的时变性引起了波流相互作用。     

垂直切变风场中声重波的谱传播

本文研究声重波在垂直切变风场中传播时谱结构的改变。根据可压缩情况下的流体力学方程组,导出垂直切变风场中大气声重波的谱方程。并指出,这个谱方程是Taylor-Goldstein方程在可压缩和任意垂直波长情况下的推广。由谱方程出发,考虑低边界上的声重波强迫为高斯谱型,采用差分方法,我们计算了ω-K_H二维空间中的高层谱响应。结果表明,在具有垂直切变的背景风场作用下,声重波的谱结构发生了改变:1.在原强迫谱所覆盖的谱区段内,一些谱成份被挖除,形成了尖锐的谱峰群;2.最大谱峰发生了偏移;3.波谱变得狭窄。这些变化是垂直切变风场对声重波谱滤波的结果。文中还将上述结论与电离层观测结果进行比较,解释了某些观测现象。     

切变基本纬向流中非线性赤道Rossby长波

为了解决观测和理论研究中的一些问题以及更好地了解热带大气动力学 ,有必要进一步研究基本气流的变化对大气中赤道Rossby波动的影响 .本文研究分析基本气流对赤道Rossby长波的影响 ,利用一个简单赤道 β平面浅水模式和摄动法 ,研究纬向基本气流切变中非线性赤道Rossby波 ,推导出在切变基本纬向流中赤道Rossby长波振幅演变所满足的非线性KdV方程并得到其孤立波解 .分析表明 ,孤立波存在的必要条件是基本气流有切变 ,而且基流切变不能太强 ,否则将产生正压不稳定 .     

ESF小尺度湍动谱簇射和非线性稳定性理论（Ⅰ）

本文从等离子体二流体方程出发,推导了适于描述赤道扩展F（ESF）层小尺度湍流的二维静电模型方程.对模型方程进行了线性分析,并且导出了描述波波相互作用的三波非线性耦合方程,以此为基础详细讨论了若干情况下的非线性稳定性和能谱簇射过程.结果表明,赤道F层不仅可以存在正能波,而且可能存在负能波;正能波和负能波的相互作用可以导致爆炸型不稳定性;各种可能的三个波（如三个正能波,二个正能波和一个负能波,等等）之间的相互作用可以产生不同类型的非线性不稳定性,导致不同形式的能量簇射,例如能量可以向大波数方向簇射,也可相反,还可能同时向大和小波数方向簇射等。     

地震多级散射波正演模拟方法

地震波在穿越地下散射体群时会产生多级散射波,分析其地震响应特征,可推断散射体的分布情况和性质。本文从二维标量波动方程出发,结合地震散射理论和波恩近似理论,推导了多级散射波方程。在此基础上,采用高阶有限差分法对双点散射体模型和复杂散射体模型进行数值模拟,分析了多级散射波的传播规律和波场特征,并通过抽取多级散射记录和各级散射记录的单道记录与参考单道记录的对比,验证了本文推导散射波方程的准确性。      

固体介质中非线性波的能量初探

本文从能源问题与勘探问题的密切关系出发，提出进行深入的非线性波研究的必要性——进一步提供可靠而详实的地质资料，以解决实际地质问题.说明了非线性科学与非线性波动的关系和特点，非线性波动是非线性科学的一个重要的分支，而地球本身的特点也决定了非线性科学是解决地质问题的重要基础.回顾了波动理论的研究历程及当今国内外非线性研究的进展情况.通过上述认识，提出了非线性波动问题中能量的重要性，然后分别从震源与冲击波的形成，界面处的能量分配，介质中能量的衰减，波的相互作用四个方面讨论了非线性波的能量问题.通过对能量问题的讨论，进一步讨论了影响非线性波能量的因素.从能量的角度出发，探讨了以后进行固体中非线性波研究的重点.最后对非线性波在地学应用中的可能性进行了探讨.     

Variations in the characteristics of acoustic gravity waves according to simulation data

The characteristics of different-scale acoustic gravity waves (wavelengths of 100–1200 km, periods of 10–50 min) under different geophysical conditions have been studied using a numerical model for calculating the vertical structure of these waves in a nonisothermal atmosphere in the presence of an altitudedependent background wind and in a situation when molecular dissipation is taken into account. It has been established that all considered acoustic gravity waves (AGWs) effectively reach altitudes of the thermosphere. The character of the amplitude vertical profile depends on the AGW scales. The seasonal and latitudinal differences in the AGW vertical structure depend on the background wind and temperature. A strong thermospheric wind causes the rapid damping of medium-scale AGWs propagating along the wind. Waves with long periods to a lesser degree depend on dissipation in the thermosphere and can penetrate to high altitudes. A change in the geomagnetic activity level affects the background wind vertical distribution at high latitudes, as a result of which the AGW vertical structure varies.     

Ranges of AGW propagation in the Earth’s atmosphere

The propagation of atmospheric gravity waves (AGWs) is studied in the context of geometrical optics in the nonisothermal, viscous, and thermal-conductive atmosphere of Earth in the presence of wind shifts. Parametric diagrams are plotted, determining the regions of allowed frequencies and horizontal phase velocities of AGWs depending on the altitude. It is shown that a part of the spectrum of AGWs propagates in stationary air in an altitude range from the Earth’s surface through the ionospheric F1 layer. AGW from nearearth sources attenuate below 250 km, while waves generated at altitudes of about 300 km and higher do not reach the Earth’s surface because of the inner reflection from the thermosphere base. The pattern changes under strong thermospheric winds. AGW dissipation decreases with an adverse wind shift and, hence, a part of the wave spectrum penetrated from the lower atmosphere to the altitudes of F2 layer.     

Formation of large-scale disturbances in the upper atmosphere caused by acoustic gravity wave sources on the Earth’s surface

The results of a model study of the acoustic gravity wave (AGW) propagation from the Earth’s surface to the upper atmospheric altitudes have been considered. Numerical calculations have been performed using a nonhydrostatic model of the atmosphere, which takes into account nonlinear and dissipative processes originating when waves propagate upward. The model source of atmospheric disturbances has been specified in an area localized on the Earth’s surface. The disturbance source frequency spectrum includes harmonics at frequencies of 0.5ωg-1.5ωg (ωg is the Brunt-Väisälä frequency near the Earth’s surface). The calculations indicated that AGW propagation and dissipation over the source result in the fact that the region of large-scale spatial disturbances of the upper atmosphere mean state is formed at ～200 km altitudes. This region substantially affects AGW propagation and results in waveguide propagation of AGWs with periods shorter than the Väisälä-Brunt period at the altitude of a disturbed atmosphere. The dissipation of AGWs propagating in such a waveguide results in a waveguide horizontal expansion. The extension of the disturbed region of the mean state of the upper atmosphere and, consequently, the waveguide length can reach ～1000 km, if the AGW ground source operates for ～1 h. The physical mechanism by which large-scale disturbances are formed in the upper atmosphere, based on the propagation and dissipation of AGWs with periods shorter than the Väisälä-Brunt period in the upper atmosphere, explains why these disturbances are rapidly generated and localized above AGW sources located on the Earth’s surface or in the lower atmosphere.     

Generalized polarization relationships for acoustic gravity waves in the nonisothermal atmosphere with the wind

The nonlinear equation of the first order of the Riccati type has been obtained for the wave impedance of acoustic gravity waves in the nonisothermal atmosphere. The vertically nonuniform horizontal wind and the effect of viscosity on the horizontal components of the velocity field have been taken into account in the calculations. The boundary-value problem for the Riccati equation is defined by the boundary emission condition at high altitudes. Upon finding the wave impedance along with the generalized polarization relationship, all remaining disturbances of the atmospheric parameters related to acoustic gravity waves are found with the help of a simple integration. The results of using a developed formalism are illustrated by the numerical computation of acoustic gravity wave fields in the atmosphere with real vertical profiles of temperature and horizontal field velocity.     

Rossby波的螺旋斑图

应用描写大气大尺度运动的准地转方程组，求得了大气Rossby波的三维定常流场以及相应的位温场、涡度场和散度场，其中的三维流场构成了物理空间的一个非线性自治动力系统. 研究表明，Rossby波具有     

2009年1月强爆发性增温期间突发E(Es)层的响应

平流层爆发性增温(SSW)期间,低层大气温度场和风场等的剧烈变化会直接影响潮汐和风剪切作用.此举可能会导致电离层Es的相应变化.本文以2009年1月事件为例,分析了SSW期间Es层的响应.首先,在排除太阳活动和地磁活动对Es层影响的前提下,分析了昆明站附近MLT区域行星波和潮汐波的波动特性,发现此期间存在显著的2日行星波,并伴有日潮汐减弱和半日潮汐增强等波动现象;随后,分析相应时间段内Es层的变化特性发现,重庆和昆明站附近Es层强度明显减弱,且其高度显著抬升.这一现象与低层大气的波动变化具有同步性.最后,通过模拟经典风剪切理论下Es层金属离子的汇聚过程和运动轨迹,再现了SSW期间Es层与低层大气波动的耦合演化过程.该分析结果为研究低层-中层-高层大气的耦合过程提供了一种新的思路.     

耗散大气中水平不均匀风场对内重力波传播的影响

采用包括耗散的射线跟踪方法，计算了在水平不均匀风场作用下，不同尺度重力波从对流层直至220km观测高度的传播，结果表明，垂直于重力波传播方向的风以及风剪切能够引起波射线的折射，从而导致重力波明显偏离初始传播方向.在强顺风场作用下，由于风场引起的捕获，大量重力波不能传播到观测高度.由于风场引起的多普勒频移，小周期的重力波在弱顺风条件下能够传播到观测高度.由于反射作用，强逆风场不支持周期低于约18min的较高频重力波的传播.而在弱逆风作用下，大部分中尺度范围重力波都能够传播到观测高度.本文统计了武汉电离层观象台的TID观测数据随热层风场的分布，统计结果与模拟结果符合较好.